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 attempted with no better success than attended the essay of David to wear the armour of Saul. Another use however is possible and of far greater promise, namely, the actual application of the positions which had so wonderfully enlarged the discoveries of geometry, mutatis mutandis, to philosophical subjects. Kant having briefly illustrated the utility of such an attempt in the questions of space, motion, and infinitely small quantities, as employed by the mathematician, proceeds to the idea of negative quantities and the transfer of them to metaphysical investigation. Opposites, he well observes, are of two kinds, either logical, i.e. such as are absolutely incompatible; or real without being contradictory. The former he denominates Nihil negativum irrepræsentabile, the connexion of which produces nonsense. A body in motion is something—Aliquid cogitabile; but a body, at one and the same time in motion and not in motion, is nothing, or at most, air articulated into nonsense. But a motory force of a body in one direction, and an equal force of the same body in an opposite direction is not incompatible, and the result, namely rest, is real and representable. For the purposes of mathematical calculus it is indifferent which force we term negative, and which positive, and consequently we appropriate the latter to that, which happens to be the principal object in our